Question

# In the expansion of (31/7+51/2)14, which of the following is true?

A
number of rational terms is 3
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B
number of irrational terms is 12
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C
the sum of last two digits of rational terms is 34
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D
seventh term is the middle term
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Solution

## The correct option is C the sum of last two digits of rational terms is 34In the expansion of (31/7+51/2)14, Tr+1= 14Cr(31/7)14−r⋅(51/2)r, r=0,1,2,…,14 = 14Cr 3(2−r7)⋅5r/2 There are only two rational terms, when r=0,14 So, rational terms are, T1=32 and T15=57 Total number of terms =14+1=15 Number of irrational terms =15−2=13 Sum of last two digits of rational terms =32+57=9+_ _ _ 25=_ _ _ 34 Since, total number of terms is 15 i.e. odd, ∴ Middle term =15+12=8

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